一类具有饱和传染率的分数阶SIR传染病模型的动力学性质  

Dynamical Properties of a class of Fractional Order SIR Epidemic Model with Saturation Incidence

作　　者：李明山 张渝曼 梁凤 黄静珊 李晓培 

机构地区：[1]岭南师范学院数学与统计学院,广东湛江524048

出　　处：《岭南师范学院学报》2017年第3期32-41,共10页Journal of Lingnan Normal University

基　　金：国家自然科学基金项目(11561019);广东省创新强校科技重大项目(2014KZDXM065);广东省大学生科技创新重点项目(pdjh2016a0301);全国大学生创新创业训练计划项目(201710579457);岭南师范学院攀峰计划项目

摘　　要：研究了一类具有饱和发生率分数阶SIR传染病模型的动力学性质.首先介绍了分数阶微分方程的基本性质与相关引理.然后通过分析特征值与系数参数的关系得到了平衡点稳定性.接着证明了该模型一致稳态正解的存在唯一性,最后考虑了具有饱和治疗函数的分数阶SIR传染病模型的平衡点稳定性及该模型一致稳态正解的存在唯一性.In this paper,we study the dynamical properties of a class of SIR epidemic model with satu-ration incidence rate. Firstly, the basic properties of the fractional differential lemmas are introduced. Then the stability of the equilibrium point is obtained by analyzing the relationship between the eigenvalue and the coefficient. Next we prove the existence and uniqueness of the positive steady-state solution of the model. At last,we consider the stability of the equilibrium point and the ex-istence and uniqueness of the positive steady-state solution of the fractional order SIR epidemic model with saturated treatment function.

关 键 词：分数阶SIR模型 饱和传染率 一致稳态解 稳定性 治疗函数 

分 类 号：O175[理学—数学]